Advanced Number Theory
Challenging explorations of number theory that delve into prime numbers and divisibility.
Description : This course offers an in‑depth exploration of number theory, inviting students to investigate prime numbers, divisibility, and other fundamental properties through rigorous analysis and creative challenges.
Category : Math
Age : 12+
Difficulty Level : Normal
Curriculum :
Module 1: Foundations of Number Theory Section 1: Understanding the Number System - Lesson 1: What Are Numbers? - Module 1, Section 1, Lesson 1 What Are Numbers? - Lesson 2: Classifying Numbers: Natural, Integer, and Rational - Module 1, Section 1, Lesson 2 Classifying Numbers: Natural, Integer, and Rational Section 2: Core Properties of Integers - Lesson 1: Even and Odd Numbers: Recognizing Differences - Module 1, Section 2, Lesson 1 Even and Odd Numbers: Recognizing Differences - Lesson 2: The Role of Zero and One in Number Theory - Module 1, Section 2, Lesson 2 The Role of Zero and One in Number Theory Section 3: Basic Arithmetic Operations - Lesson 1: Fundamentals of Addition and Subtraction - Module 1, Section 3, Lesson 1 Fundamentals of Addition and Subtraction - Lesson 2: Introduction to Multiplication and Division - Module 1, Section 3, Lesson 2 Introduction to Multiplication and Division Section 4: The Number Line and Magnitude - Lesson 1: Understanding the Number Line - Module 1, Section 4, Lesson 1 Understanding the Number Line - Lesson 2: Visualizing Size and Order of Numbers - Module 1, Section 4, Lesson 2 Visualizing Size and Order of Numbers Section 5: Mathematical Notation and Language - Lesson 1: Symbols and Conventions in Number Theory - Module 1, Section 5, Lesson 1 Symbols and Conventions in Number Theory - Lesson 2: Writing and Interpreting Mathematical Statements - Module 1, Section 5, Lesson 2 Writing and Interpreting Mathematical Statements Module 2: Divisibility and Factorization Basics Section 1: Introduction to Divisibility - Lesson 1: What Is Divisibility? - Module 2, Section 1, Lesson 1 What Is Divisibility? - Lesson 2: Simple Divisibility Rules and Their Uses - Module 2, Section 1, Lesson 2 Simple Divisibility Rules and Their Uses Section 2: Factors and Multiples - Lesson 1: Identifying Factors of a Number - Module 2, Section 2, Lesson 1 Identifying Factors of a Number - Lesson 2: Understanding Multiples and Their Patterns - Module 2, Section 2, Lesson 2 Understanding Multiples and Their Patterns Section 3: Fundamentals of Prime Numbers - Lesson 1: What Makes a Number Prime? - Module 2, Section 3, Lesson 1 What Makes a Number Prime? - Lesson 2: Recognizing Prime Numbers in Everyday Contexts - Module 2, Section 3, Lesson 2 Recognizing Prime Numbers in Everyday Contexts Section 4: Factor Trees and Decomposition - Lesson 1: Constructing Factor Trees - Module 2, Section 4, Lesson 1 Constructing Factor Trees - Lesson 2: Exploring the Unique Factorization Principle - Module 2, Section 4, Lesson 2 Exploring the Unique Factorization Principle Section 5: Practical Applications of Divisibility - Lesson 1: Divisibility in Simple Problem Solving - Module 2, Section 5, Lesson 1 Divisibility in Simple Problem Solving - Lesson 2: Puzzles and Games Using Divisibility - Module 2, Section 5, Lesson 2 Puzzles and Games Using Divisibility Module 3: Prime Numbers and Their Properties Section 1: In-Depth Look at Prime Numbers - Lesson 1: Essential Properties of Prime Numbers - Module 3, Section 1, Lesson 1 Essential Properties of Prime Numbers - Lesson 2: Why Prime Numbers Matter in Mathematics - Module 3, Section 1, Lesson 2 Why Prime Numbers Matter in Mathematics Section 2: Methods of Primality Testing - Lesson 1: Simple Methods for Testing Primality - Module 3, Section 2, Lesson 1 Simple Methods for Testing Primality - Lesson 2: Introduction to the Sieve of Eratosthenes - Module 3, Section 2, Lesson 2 Introduction to the Sieve of Eratosthenes Section 3: Techniques of Prime Factorization - Lesson 1: Step-by-Step Prime Factorization - Module 3, Section 3, Lesson 1 Step-by-Step Prime Factorization - Lesson 2: Verifying Factorizations and Their Uniqueness - Module 3, Section 3, Lesson 2 Verifying Factorizations and Their Uniqueness Section 4: The Role of Primes in Equations - Lesson 1: How Primes Influence Equation Solutions - Module 3, Section 4, Lesson 1 How Primes Influence Equation Solutions - Lesson 2: Recognizing Patterns Involving Prime Numbers - Module 3, Section 4, Lesson 2 Recognizing Patterns Involving Prime Numbers Section 5: Historical Perspectives on Prime Numbers - Lesson 1: Ancient Views and Discoveries of Primes - Module 3, Section 5, Lesson 1 Ancient Views and Discoveries of Primes - Lesson 2: Evolution of Prime Number Theory Over Time - Module 3, Section 5, Lesson 2 Evolution of Prime Number Theory Over Time Module 4: Modular Arithmetic and Congruences Section 1: Introduction to Modular Arithmetic - Lesson 1: Understanding the Modulo Operation - Module 4, Section 1, Lesson 1 Understanding the Modulo Operation - Lesson 2: Everyday Applications of Modular Thinking - Module 4, Section 1, Lesson 2 Everyday Applications of Modular Thinking Section 2: Grasping Congruence Relations - Lesson 1: Basics of Congruence in Number Theory - Module 4, Section 2, Lesson 1 Basics of Congruence in Number Theory - Lesson 2: Properties and Simple Examples of Congruence - Module 4, Section 2, Lesson 2 Properties and Simple Examples of Congruence Section 3: Exploring Remainders - Lesson 1: Techniques for Calculating Remainders - Module 4, Section 3, Lesson 1 Techniques for Calculating Remainders - Lesson 2: Patterns Observed in Remainder Calculations - Module 4, Section 3, Lesson 2 Patterns Observed in Remainder Calculations Section 4: Solving Simple Modular Equations - Lesson 1: Step-by-Step Methods for Modular Equations - Module 4, Section 4, Lesson 1 Step-by-Step Methods for Modular Equations - Lesson 2: Practice Problems in Modular Arithmetic - Module 4, Section 4, Lesson 2 Practice Problems in Modular Arithmetic Section 5: Applications of Modular Arithmetic - Lesson 1: An Introduction to Modular Arithmetic in Cryptography - Module 4, Section 5, Lesson 1 An Introduction to Modular Arithmetic in Cryptography - Lesson 2: Recognizing Cycles and Patterns in Modular Systems - Module 4, Section 5, Lesson 2 Recognizing Cycles and Patterns in Modular Systems Module 5: Patterns, Logic, and Applications in Number Theory Section 1: Recognizing Patterns in Numbers - Lesson 1: Observing Patterns in Numerical Sequences - Module 5, Section 1, Lesson 1 Observing Patterns in Numerical Sequences - Lesson 2: Developing Skills in Pattern Recognition - Module 5, Section 1, Lesson 2 Developing Skills in Pattern Recognition Section 2: Introduction to Logical Reasoning - Lesson 1: Basic Logical Reasoning in Mathematics - Module 5, Section 2, Lesson 1 Basic Logical Reasoning in Mathematics - Lesson 2: Using Logic to Validate Number Theory Concepts - Module 5, Section 2, Lesson 2 Using Logic to Validate Number Theory Concepts Section 3: Problem Solving Strategies in Number Theory - Lesson 1: Approaches to Tackling Number Theory Problems - Module 5, Section 3, Lesson 1 Approaches to Tackling Number Theory Problems - Lesson 2: Breaking Down Complex Problems into Steps - Module 5, Section 3, Lesson 2 Breaking Down Complex Problems into Steps Section 4: Applying Fundamental Theorems - Lesson 1: Introduction to the Fundamental Theorem of Arithmetic - Module 5, Section 4, Lesson 1 Introduction to the Fundamental Theorem of Arithmetic - Lesson 2: Practical Applications of Fundamental Concepts - Module 5, Section 4, Lesson 2 Practical Applications of Fundamental Concepts Section 5: Review and Creative Challenges - Lesson 1: Recap of Essential Number Theory Ideas - Module 5, Section 5, Lesson 1 Recap of Essential Number Theory Ideas - Lesson 2: Creative Challenges and Exploration in Number Theory - Module 5, Section 5, Lesson 2 Creative Challenges and Exploration in Number Theory